Properties

Label 12.5.d
Level 12
Weight 5
Character orbit d
Rep. character \(\chi_{12}(7,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(12, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\(4q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 108q^{9} \) \(\mathstrut -\mathstrut 172q^{10} \) \(\mathstrut +\mathstrut 180q^{12} \) \(\mathstrut +\mathstrut 296q^{13} \) \(\mathstrut +\mathstrut 600q^{14} \) \(\mathstrut +\mathstrut 112q^{16} \) \(\mathstrut -\mathstrut 600q^{17} \) \(\mathstrut -\mathstrut 162q^{18} \) \(\mathstrut -\mathstrut 1368q^{20} \) \(\mathstrut -\mathstrut 144q^{21} \) \(\mathstrut -\mathstrut 1128q^{22} \) \(\mathstrut +\mathstrut 1296q^{24} \) \(\mathstrut +\mathstrut 972q^{25} \) \(\mathstrut +\mathstrut 1692q^{26} \) \(\mathstrut +\mathstrut 1488q^{28} \) \(\mathstrut +\mathstrut 888q^{29} \) \(\mathstrut -\mathstrut 1980q^{30} \) \(\mathstrut -\mathstrut 2784q^{32} \) \(\mathstrut +\mathstrut 720q^{33} \) \(\mathstrut -\mathstrut 484q^{34} \) \(\mathstrut +\mathstrut 540q^{36} \) \(\mathstrut -\mathstrut 4408q^{37} \) \(\mathstrut +\mathstrut 4680q^{38} \) \(\mathstrut +\mathstrut 1664q^{40} \) \(\mathstrut +\mathstrut 552q^{41} \) \(\mathstrut -\mathstrut 2088q^{42} \) \(\mathstrut -\mathstrut 3696q^{44} \) \(\mathstrut -\mathstrut 648q^{45} \) \(\mathstrut -\mathstrut 384q^{46} \) \(\mathstrut +\mathstrut 1008q^{48} \) \(\mathstrut -\mathstrut 572q^{49} \) \(\mathstrut -\mathstrut 1038q^{50} \) \(\mathstrut +\mathstrut 6008q^{52} \) \(\mathstrut +\mathstrut 5112q^{53} \) \(\mathstrut +\mathstrut 486q^{54} \) \(\mathstrut +\mathstrut 1728q^{56} \) \(\mathstrut +\mathstrut 5616q^{57} \) \(\mathstrut -\mathstrut 124q^{58} \) \(\mathstrut -\mathstrut 2664q^{60} \) \(\mathstrut +\mathstrut 4232q^{61} \) \(\mathstrut -\mathstrut 7224q^{62} \) \(\mathstrut -\mathstrut 14720q^{64} \) \(\mathstrut -\mathstrut 18192q^{65} \) \(\mathstrut +\mathstrut 4824q^{66} \) \(\mathstrut +\mathstrut 5496q^{68} \) \(\mathstrut -\mathstrut 9792q^{69} \) \(\mathstrut +\mathstrut 6096q^{70} \) \(\mathstrut +\mathstrut 8840q^{73} \) \(\mathstrut -\mathstrut 4116q^{74} \) \(\mathstrut -\mathstrut 1872q^{76} \) \(\mathstrut +\mathstrut 20928q^{77} \) \(\mathstrut +\mathstrut 9900q^{78} \) \(\mathstrut +\mathstrut 25632q^{80} \) \(\mathstrut +\mathstrut 2916q^{81} \) \(\mathstrut +\mathstrut 3740q^{82} \) \(\mathstrut -\mathstrut 10512q^{84} \) \(\mathstrut -\mathstrut 10256q^{85} \) \(\mathstrut -\mathstrut 19560q^{86} \) \(\mathstrut -\mathstrut 8640q^{88} \) \(\mathstrut -\mathstrut 25080q^{89} \) \(\mathstrut +\mathstrut 4644q^{90} \) \(\mathstrut +\mathstrut 18816q^{92} \) \(\mathstrut -\mathstrut 17136q^{93} \) \(\mathstrut -\mathstrut 5232q^{94} \) \(\mathstrut -\mathstrut 8352q^{96} \) \(\mathstrut +\mathstrut 23048q^{97} \) \(\mathstrut -\mathstrut 5850q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(12, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.5.d.a \(4\) \(1.240\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(6\) \(0\) \(24\) \(0\) \(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)